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Discrete mathematics and algebra MT3170

This course is intended to give an introduction to the areas of mathematics known as discrete mathematics and the study of modern algebra.

A key aim is to provide an insight into the interactions between these areas, in particular to modern applications such as coding and cryptography.


If taken as part of a BSc degree, courses which must be passed before this courses may be attempted:

  • MT2116 Abstract mathematics.

Topics covered

This full course develops the mathematical methods of discrete mathematics and algebra and will emphasis their applications.

  • Counting: selections, inclusion-exclusion, partitions and permutations, Stirling numbers, generating functions, recurrence relations.
  • Graph Theory: basic concepts (graph, adjacency matrix, etc.), walks and cycles, trees and forests, colourings.
  • Set Systems: matching, finite geometries, block designs.
  • Abstract groups: revision of key concepts such as cyclic groups, subgroups, homomorphisms and Lagrange’s theorem. Conjugation and normal subgroups. Group actions.
  • Applications of algebra to discrete mathematics I: permutations, orbits and stabilisers, the orbit-stabiliser theorem; applications to counting problems.
  • Rings and polynomials: the Euclidean algorithm for polynomials, integral domains, ideals, factor rings, fields, field extensions.
  • Finite fields: construction, the primitive element theorem, and finite linear algebra.
  • Applications of algebra to discrete mathematics II: finite Geometry: designs, affine and projective planes.
  • Error-correcting codes: linear codes, cyclic codes, perfect codes.

Learning outcomes

If you complete the course successfully, you should be able to:

  • Demonstrate knowledge definitions, concepts and methods in the topics covered and how to apply these
  • Find and formulate simple proofs
  • Model situations in a mathematical way and derive useful results.


Unseen written exam (3 hrs).

Essential reading

  • Biggs, N. Discrete mathematics. Oxford: Oxford University Press, 2002.
  • Cameron, P.J. Introduction to Algebra. Oxford: Oxford University Press, 2008.
  • Cameron, P.J. Combinatorics. Oxford: Oxford University Press, 2008.

Course information sheets

Download the course information sheets from the LSE website.